# Table 9: Augmented Local Projections — Pre-Trend Fix

Adding y_{t-1} and y_{t-2} as controls absorbs pre-existing trends.
Spec C also adds lagged GDP growth.


## Investment/GDP

| h | A: Unadjusted | B: + 2 lags of y | C: + 2 lags + lag growth |
|---|---|---|---|
| -3 | -0.2729 (N=703) | -0.1240 (N=703) | -0.1828 (N=703) |
| -2 | -0.5237* (N=703) | 0.0000*** (N=703) | 0.0000*** (N=703) |
| -1 | -0.8874*** (N=703) | 0.0000*** (N=703) | 0.0000*** (N=703) |
| 0 | -1.6546*** (N=703) | -0.2279 (N=703) | 0.0201 (N=703) |
| 1 | 0.1071 (N=703) | 0.1034 (N=703) | 0.2296 (N=703) |
| 2 | 0.6917** (N=703) | 0.7692** (N=703) | 0.4989 (N=703) |
| 3 | 0.2045 (N=703) | 0.1930 (N=703) | 0.2661 (N=703) |
| 4 | -0.3329 (N=703) | -0.4718 (N=703) | -0.3167 (N=703) |
| 5 | -0.5454 (N=703) | -0.5016 (N=703) | -0.5457 (N=703) |


## GDP Growth

| h | A: Unadjusted | B: + 2 lags of y |
|---|---|---|
| -3 | -2.6736*** (N=703) | -0.8864*** (N=703) |
| -2 | -2.3669*** (N=703) | -0.0000 (N=703) |
| -1 | -1.4518*** (N=703) | 0.0000*** (N=703) |
| 0 | -1.2573*** (N=703) | -3.1279*** (N=703) |
| 1 | 0.4642 (N=703) | 0.2884 (N=703) |
| 2 | 1.7783** (N=703) | 0.9636 (N=703) |
| 3 | 1.8344** (N=703) | 0.8528 (N=703) |
| 4 | 0.0104 (N=703) | -1.4758** (N=703) |
| 5 | 0.3055 (N=703) | -0.9881 (N=703) |


## MPK

| h | A: Unadjusted | B: + 2 lags of y | C: + 2 lags + lag growth |
|---|---|---|---|
| -3 | 0.0004 (N=703) | 0.0017*** (N=703) | 0.0017*** (N=703) |
| -2 | 0.0009 (N=703) | -0.0000** (N=703) | 0.0000*** (N=703) |
| -1 | 0.0021** (N=703) | -0.0000*** (N=703) | 0.0000*** (N=703) |
| 0 | -0.0019*** (N=703) | -0.0012** (N=703) | -0.0013** (N=703) |
| 1 | 0.0052*** (N=666) | 0.0053*** (N=666) | 0.0050*** (N=666) |
| 2 | 0.0031*** (N=629) | 0.0032*** (N=629) | 0.0026** (N=629) |
| 3 | 0.0010 (N=592) | 0.0010 (N=592) | 0.0017 (N=592) |
| 4 | -0.0027** (N=555) | -0.0029** (N=555) | -0.0030** (N=555) |
| 5 | -0.0018 (N=518) | -0.0022* (N=518) | -0.0024** (N=518) |


## Δlog K/L

| h | A: Unadjusted | B: + 2 lags of y | C: + 2 lags + lag growth |
|---|---|---|---|
| -3 | -0.0019 (N=703) | -0.0005 (N=703) | 0.0004 (N=703) |
| -2 | -0.0006 (N=703) | 0.0000*** (N=703) | -0.0000*** (N=703) |
| -1 | -0.0010 (N=703) | -0.0000*** (N=703) | 0.0000** (N=703) |
| 0 | 0.0064*** (N=703) | 0.0040** (N=703) | -0.0003 (N=703) |
| 1 | -0.0060* (N=666) | -0.0052 (N=666) | -0.0042 (N=666) |
| 2 | -0.0157*** (N=629) | -0.0145*** (N=629) | -0.0140*** (N=629) |
| 3 | -0.0138*** (N=592) | -0.0126*** (N=592) | -0.0120*** (N=592) |
| 4 | -0.0078* (N=555) | -0.0068 (N=555) | -0.0053 (N=555) |
| 5 | -0.0082 (N=518) | -0.0070 (N=518) | -0.0061 (N=518) |


```
A: Unadjusted: Demo Inflows → Investment/GDP (OECD)
===================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3      -0.27291  0.28318 0.3355    703                         ---------·---------                  
 -2     -0.52374*  0.27154 0.0542    703                     ---------o--------                       
 -1   -0.88743***  0.27252 0.0012    703               ---------*--------     |                       
  0   -1.65463***  0.30187 0.0000    703  ---------*----------                |                       
  1       0.10712  0.31194 0.7314    703                              ----------·----------           
  2     0.69170**  0.34238 0.0437    703                                      |-----------*-----------
  3       0.20450  0.34535 0.5539    703                              ------------·-----------        
  4      -0.33285  0.34401 0.3336    703                      -----------·-----------                 
  5      -0.54542  0.34358 0.1129    703                  -----------·-----------                     
                                          ------------------------------------------------------------
        -2.2463                                            1.3628
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

B: + 2 lags of y: Demo Inflows → Investment/GDP (OECD)
======================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3      -0.12402  0.13496 0.3584    703                   ------·------                              
 -2    0.00000***  0.00000 0.0000    703                            *                                 
 -1    0.00000***  0.00000 0.0000    703                            *                                 
  0      -0.22793  0.17053 0.1818    703               --------·-------                               
  1       0.10337  0.31206 0.7406    703                 -------------·--------------                 
  2     0.76921**  0.33889 0.0235    703                            | ---------------*----------------
  3       0.19303  0.34771 0.5790    703                 ---------------·----------------             
  4      -0.47180  0.34748 0.1750    703  ---------------·----------------                            
  5      -0.50156  0.34318 0.1443    703  ---------------·---------------                             
                                          ------------------------------------------------------------
        -1.1742                                            1.4334
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

C: + 2 lags + lag growth: Demo Inflows → Investment/GDP (OECD)
==============================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3      -0.18279  0.13343 0.1712    703                     ------·-------                           
 -2    0.00000***  0.00000 0.0000    703                                *                             
 -1    0.00000***  0.00000 0.0000    703                                *                             
  0       0.02013  0.15459 0.8964    703                         -------·--------                     
  1       0.22958  0.31253 0.4628    703                      ----------------·---------------        
  2       0.49889  0.33515 0.1371    703                            ----------------·-----------------
  3       0.26609  0.35026 0.4477    703                     -----------------·-----------------      
  4      -0.31670  0.34765 0.3626    703       -----------------·-----------------                    
  5      -0.54574  0.34621 0.1154    703  ----------------·-----------------                          
                                          ------------------------------------------------------------
        -1.2243                                            1.1558
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

A: Unadjusted: Demo Inflows → GDP Growth (OECD)
===============================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3   -2.67360***  0.66953 0.0001    703  ----------*-----------          |                           
 -2   -2.36687***  0.54632 0.0000    703      ---------*--------          |                           
 -1   -1.45182***  0.29133 0.0000    703                 -----*-----      |                           
  0   -1.25728***  0.30303 0.0000    703                   -----*----     |                           
  1       0.46419  0.60236 0.4412    703                            ----------·---------              
  2     1.77830**  0.71798 0.0135    703                                  |  -----------*------------ 
  3     1.83443**  0.75098 0.0148    703                                  |  ------------*------------
  4       0.01042  0.80171 0.9896    703                     -------------·-------------              
  5       0.30547  0.81055 0.7064    703                       -------------·-------------            
                                          ------------------------------------------------------------
        -3.9859                                            3.3064
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

B: + 2 lags of y: Demo Inflows → GDP Growth (OECD)
==================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3   -0.88642***  0.25273 0.0005    703                         -----*-----  |                       
 -2      -0.00000  0.00000 0.2504    703                                      ·                       
 -1    0.00000***  0.00000 0.0081    703                                      *                       
  0   -3.12791***  0.39948 0.0000    703  -------*-------                     |                       
  1       0.28839  0.63009 0.6473    703                              -----------·------------        
  2       0.96358  0.69917 0.1686    703                                   -------------·-------------
  3       0.85282  0.71211 0.2315    703                                 --------------·------------- 
  4    -1.47578**  0.72581 0.0424    703           --------------*-------------                       
  5      -0.98814  0.74779 0.1868    703               --------------·--------------                  
                                          ------------------------------------------------------------
        -3.9109                                            2.3340
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

A: Unadjusted: Demo Inflows → MPK (OECD)
========================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3       0.00038  0.00112 0.7342    703                -----------·-----------                       
 -2       0.00092  0.00111 0.4036    703                   -----------·----------                     
 -1     0.00213**  0.00105 0.0424    703                         |---------*----------                
  0   -0.00192***  0.00071 0.0074    703         -------*------- |                                    
  1    0.00521***  0.00107 0.0000    666                         |              ----------*-----------
  2    0.00313***  0.00110 0.0045    629                         |    ----------*-----------          
  3       0.00103  0.00114 0.3665    592                   -----------·-----------                    
  4    -0.00266**  0.00114 0.0200    555  ----------*----------- |                                    
  5      -0.00184  0.00118 0.1196    518     -----------·-----------                                  
                                          ------------------------------------------------------------
        -0.0049                                            0.0073
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

B: + 2 lags of y: Demo Inflows → MPK (OECD)
===========================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3    0.00174***  0.00049 0.0004    703                          |  -----*----                       
 -2    -0.00000**  0.00000 0.0346    703                          *                                   
 -1   -0.00000***  0.00000 0.0005    703                          *                                   
  0    -0.00116**  0.00056 0.0389    703               -----*-----|                                   
  1    0.00527***  0.00107 0.0000    666                          |              ----------*----------
  2    0.00321***  0.00110 0.0038    629                          |    ----------*----------          
  3       0.00104  0.00114 0.3608    592                    -----------·----------                    
  4    -0.00285**  0.00115 0.0131    555  ----------*-----------  |                                   
  5     -0.00222*  0.00120 0.0638    518    -----------o-----------                                   
                                          ------------------------------------------------------------
        -0.0051                                            0.0074
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

C: + 2 lags + lag growth: Demo Inflows → MPK (OECD)
===================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3    0.00169***  0.00050 0.0008    703                          |   -----*----                      
 -2    0.00000***  0.00000 0.0000    703                          *                                   
 -1    0.00000***  0.00000 0.0000    703                          *                                   
  0    -0.00127**  0.00057 0.0257    703               -----*------                                   
  1    0.00500***  0.00109 0.0000    666                          |             ----------*-----------
  2     0.00262**  0.00111 0.0191    629                          |  ----------*----------            
  3       0.00175  0.00114 0.1259    592                        -----------·-----------               
  4    -0.00297**  0.00116 0.0108    555  ----------*-----------  |                                   
  5    -0.00239**  0.00121 0.0494    518    -----------*-----------                                   
                                          ------------------------------------------------------------
        -0.0052                                            0.0071
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

A: Unadjusted: Demo Inflows → Δlog K/L (OECD)
=============================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3      -0.00195  0.00397 0.6235    703                         --------------·-------------         
 -2      -0.00058  0.00336 0.8631    703                              -----------·------------        
 -1      -0.00101  0.00203 0.6189    703                                  ------·-------              
  0    0.00636***  0.00214 0.0030    703                                          |   -------*--------
  1     -0.00596*  0.00337 0.0769    666                    ------------o-----------                  
  2   -0.01566***  0.00397 0.0001    629  -------------*--------------            |                   
  3   -0.01382***  0.00434 0.0015    592   ---------------*---------------        |                   
  4     -0.00775*  0.00465 0.0959    555             ----------------o----------------                
  5      -0.00817  0.00497 0.1011    518           -----------------·-----------------                
                                          ------------------------------------------------------------
        -0.0234                                            0.0105
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

B: + 2 lags of y: Demo Inflows → Δlog K/L (OECD)
================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3      -0.00052  0.00116 0.6509    703                                       -----·----             
 -2    0.00000***  0.00000 0.0000    703                                             *                
 -1   -0.00000***  0.00000 0.0000    703                                             *                
  0     0.00399**  0.00197 0.0435    703                                             --------*--------
  1      -0.00518  0.00326 0.1129    666                      ------------·-------------              
  2   -0.01449***  0.00366 0.0001    629  --------------*--------------              |                
  3   -0.01263***  0.00401 0.0017    592    ----------------*---------------         |                
  4      -0.00682  0.00431 0.1144    555              -----------------·-----------------             
  5      -0.00703  0.00456 0.1238    518             ------------------·------------------            
                                          ------------------------------------------------------------
        -0.0217                                            0.0079
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

C: + 2 lags + lag growth: Demo Inflows → Δlog K/L (OECD)
========================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
 -3       0.00037  0.00117 0.7509    703                                                ------·-----  
 -2   -0.00000***  0.00000 0.0001    703                                                     *        
 -1     0.00000**  0.00000 0.0109    703                                                     *        
  0      -0.00032  0.00103 0.7563    703                                               -----·-----    
  1      -0.00423  0.00329 0.1982    666                           ----------------·---------------   
  2   -0.01401***  0.00370 0.0002    629  -----------------*-----------------                |        
  3   -0.01198***  0.00405 0.0032    592     -------------------*-------------------         |        
  4      -0.00529  0.00433 0.2222    555                    --------------------·---------------------
  5      -0.00614  0.00460 0.1825    518                ----------------------·---------------------- 
                                          ------------------------------------------------------------
        -0.0213                                            0.0032
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

```

*p<0.1, **p<0.05, ***p<0.01. OECD subsample. PanelGLS with AR(1).*
